What are differences between the Salem witch trials and McCarthyism?

In the Salem Witch Trials, the stakes were far greater than in the McCarthy-era trials, as people could receive the death penalty in the Salem Trials.  Twenty people were executed in these trials, the majority of them by hanging.  These people were predominantly female, and, while there were other events similar to it in other Northeastern towns and in Europe, the Salem Witchcraft Trials happened in Salem.  The McCarthy trials did not actually kill anyone, but ruined the careers of many prominent politicians and entertainers.  The victims were predominantly men, as men made up the majority of America's political leadership of the time. Also, McCarthy focused his attention on Washington D.C., but he claimed that the entire nation was infested with Communism and it was his job to stamp it out.  

College Algebra, Chapter 1, 1.2, Section 1.2, Problem 60

Suppose that a woman driving a car $14 ft$ long is passing a truck $30 ft$ long. The truck is traveling at $50 mi/hr$. How fast must a woman drive her car so that she can pass the truck completely in $6s$?

To be consistent with the units, let us use feet and seconds instead of miles and hours.

Since both cyclists are traveling towards each other, the effective speed will be $2x + x = 3x$.

So the speed of the truck, $\displaystyle 50 \frac{mi}{hr} \left( \frac{5280 ft}{mi} \right) \left( \frac{1 hr}{3600 s} \right) = \frac{220}{3} ft/s$

Thus, in $6$ seconds, the truck travels $\displaystyle \left( \frac{220}{3} \right) \left( \frac{ft}{s} \right) (6s) = 440 ft$

Therefore, in order for the woman's car to pass the truck completely, (up to the back bumper), the distance it should traveled is $440 ft + 30 ft$ (length of the truck) $+ 14 ft$ (length of the car) $= 484 ft$.

Hence, the speed of the car must be..


$
\begin{equation}
\begin{aligned}

V = \frac{d}{dt} =& \frac{484 ft}{6s} \left( \frac{1 mi}{5280 mi} \right) \left( \frac{3600 s}{1 h} \right)
\\
\\
=& 55 \frac{mi}{hr}


\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 2, 2.2, Section 2.2, Problem 17

Given: s(t)=t^3+5t^2-3t+8
The derivative is: s'(t)=3t^2+10t-3

How does Estelle's obsession with approval from others corrupt her moral character? Please give examples with quotes.

Even though she has landed in hell, Estelle seems to have no ability to recognize her faults and wants to be admired for her beauty and charm. Upon her arrival, she tells Garcin and Inez that she suspects that she is the victim of a mistake and does not belong there at all. Because she wants them to think highly of her, she conjectures that "Stupid employees who don't know their job" have sent her there and tells them that "if they made a mistake in my case, they may have done the same about you." She tries to convince them of her goodness by telling them that she sacrificed her youth "to a man nearly three times" her age and then died of pneumonia after refusing to run off with another man. However, the truth comes out: Estelle is actually responsible for provoking the suicide of an impoverished man who loved her, whom she callously rejected. Moreover, she killed the infant they had together. Once this ugly truth is forced from her by Inez and Garcin, she tells Garcin, "I loathe you."

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 17

Find the derivative of $\displaystyle f(x) = \frac{1}{2}x - \frac{1}{3}$ using the definition and the domain of its derivative.

Using the definition of derivative


$
\begin{equation}
\begin{aligned}

\qquad f'(x) =& \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}
&&
\\
\\
\qquad f'(x) =& \lim_{h \to 0} \frac{\displaystyle \frac{x + h }{2} - \frac{1}{3} - \left( \frac{x}{2} - \frac{1}{3}\right)}{h}
&& \text{Substitute $f(x + h)$ and $f(x)$}
\\
\\
\qquad f'(x) =& \lim_{h \to 0} \frac{\displaystyle \cancel{\frac{x}{2}} + \frac{h}{2} - \cancel{\frac{1}{3}} - \cancel{\frac{x}{2}} + \cancel{\frac{1}{3}}}{h}
&& \text{Combine like terms}
\\
\\
\qquad f'(x) =& \lim_{h \to 0} \frac{\cancel{h}}{2\cancel{h}}
&& \text{Cancel out like terms}

\end{aligned}
\end{equation}
$


$\qquad \fbox{$ f'(x) = \displaystyle \frac{1}{2}$}$

Both $f(x)$ and $f'(x)$ are linear functions that extend in every number. Therefore, their domain is $(-\infty, \infty)$

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 6

Given dy/dx+2y/x=3x-5
y'+2y/x=3x-5
when the first order linear ordinary Differentian equation has the form of
y'+p(x)y=q(x)
then the general solution is ,
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
so,
y'+2y/x=3x-5--------(1)
y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = 2/x and q(x)=3x-5
so on solving with the above general solution we get:
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
=((int e^(int 2/x dx) *(3x-5)) dx +c)/e^(int 2/x dx)
first we shall solve
e^(int 2/x dx)=e^(2ln(x)) =x^2
so
proceeding further, we get
y(x) =((int e^(int 2/x dx) *(3x-5)) dx +c)/e^(int 2/x dx)
=((int x^2 *(3x-5)) dx +c)/x^2
=((int (3x^3 -5x^2) ) dx +c)/x^2
= (3x^4 /4 -5x^3/3+c)/x^2
so y(x)=(3x^4 /4 -5x^3/3+c)/(x^2 )

Why is the sniper the only character that the author describes in great detail?

Part of what makes this story's surprise ending so compelling is the fact that it never, for one moment, seemed like the sniper could be taking aim at his own brother. The protagonist sniper is so focused on what he is doing, how he is feeling, what he is seeing, that he does not seem to consider the humanity of the other sniper across the street, at least not until that other sniper is dead. He thinks of the sniper across the street as "His enemy" only; the car that pulls up is "an enemy car." When he successfully shoots the sniper across the street, he feels relief first. The narrator says,

His enemy had been hit. He was reeling over the parapet in his death agony. He struggled to keep his feet, but he was slowly falling forward as if in a dream [....]. The body turned over and over in space and hit the ground with a dull thud.

Again, the other sniper is "His enemy," and the other sniper's body is not even "his" but "the body." Such language seems to mimic what a person's mind has to do, the distance it must create, in order to make violence possible. If one needs to prepare oneself to kill another person, one has to dehumanize that person; one cannot consider their humanity or they become a great deal harder to kill. The lack of details regarding anyone aside from the protagonist sniper helps to reinforce this.

I think one reason for describing only the Republican sniper in great detail is because he is the story's protagonist.  Authors generally spend more time describing their main character because readers will spend the most time with that character.  Greater detail allows readers to feel more familiar with the character.  
Additionally, by not describing the other characters in detail, readers essentially feel about them the same way that the protagonist feels about them.  They are targets.  It doesn't matter what they look like, who they are, or what they feel.  They are enemy combatants, and they need to die.  By not describing them in detail, readers are able to have a cold detachment from them.  That's the attitude that the protagonist has about them.  We feel and sympathize with the sniper because we feel we know him better than the other characters.